Re: Help me please to resolve this equation.
- From: Robert Israel <israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Wed, 15 Aug 2007 16:25:51 -0500
marozeau@xxxxxxxxx writes:
Hello Every one:
I have the following equation
f(t) = X/(1-e^(-t/Y))
where X and Y are unknown, and e^z stand for exponential of z (e power
z).
I know two points of this function. Lets says f(t1) = s1, and f(t2) =
s2; where t1 and t2 are not zeros value.
So we got two equations:
s1 = X/(1-e^(-t1/Y))
and
s2 = X/(1-e^(-t2/Y))
Two equations and two unknowns, we should be able to resolve these
equations analytically, but I don't know how....
I should be fairly simple, but I am lost.
Not so simple.
If you divide the first equation by the second, you eliminate X and get
s1/s2 = (1-exp(-t2/Y))/(1-exp(-t1/Y))
If Z = exp(-t1/Y), t = t2/t1, s = s2/s1, you can write this as
Z = 1 - (1-Z^t) s
The general solution to this (other than the trivial Z=1) won't be nice
(unless, say, r happens to be 2 or 3), although series solutions may be possible.
--
Robert Israel israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.
- References:
- Help me please to resolve this equation.
- From: marozeau
- Help me please to resolve this equation.
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